Problem: Reduce to lowest terms: $- \dfrac{1}{5} \div - \dfrac{2}{9} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{2}{9}$ is $- \dfrac{9}{2}$ Therefore: $ - \dfrac{1}{5} \div - \dfrac{2}{9} = - \dfrac{1}{5} \times - \dfrac{9}{2} $ $ \phantom{- \dfrac{1}{5} \times - \dfrac{9}{2}} = \dfrac{-1 \times -9}{5 \times 2} $ $ \phantom{- \dfrac{1}{5} \times - \dfrac{9}{2}} = \dfrac{9}{10} $